A058942 - OEIS

%I #31 Mar 19 2020 11:06:41

%S 1,1,1,2,4,2,8,22,20,6,56,184,224,120,24,608,2248,3272,2352,840,120,

%T 9440,38080,62768,54336,26208,6720,720,198272,856480,1550528,1531344,

%U 896064,312480,60480,5040,5410688,24719488,48207488,52633344,35371776

%N Triangle of coefficients of Gandhi polynomials.

%C (1+x)^2 divides these polynomials for n > 2. - _T. D. Noe_, Jan 01 2008

%H T. D. Noe, <a href="/A058942/b058942.txt">Rows n = 1..50 of triangle, flattened</a>

%F C_1(x) = 1; C_n(x) = (x+1)*((x+1)*C_n-1(x+1) - x*C_n-1(x)).

%F Triangle T(n, k), read by rows; given by [1, 1, 4, 4, 9, 9, 16, 16, 25, ...] DELTA [1, 1, 2, 2, 3, 3, 4, 4, 5, 5, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Feb 24 2005

%e Triangle starts:

%e [1]

%e [1,      1]

%e [2,      4,      2]

%e [8,      22,     20,      6]

%e [56,     184,    224,     120,     24]

%e [608,    2248,   3272,    2352,    840,    120]

%e [9440,   38080,  62768,   54336,   26208,  6720,   720]

%e [198272, 856480, 1550528, 1531344, 896064, 312480, 60480, 5040]

%t c[1][x_] = 1; c[n_][x_] :=  c[n][x] = (x+1)*((x+1)*c[n-1][x+1] - x*c[n-1][x]); Table[ CoefficientList[ c[n][x], x], {n, 9}] // Flatten (* _Jean-François Alcover_, Oct 09 2012 *)

%o (Sage) # uses[delehamdelta from A084938]

%o def A058942_triangle(n) :

%o     A = [((i+1)//2)^2 for i in (1..n)]

%o     B = [((i+1)//2) for i in (1..n)]

%o     return delehamdelta(A, B)

%o A058942_triangle(10) # _Peter Luschny_, Nov 09 2019

%Y First column is A005439, as are row sums. See also A036970.

%Y Cf. A084938.

%K nonn,tabl,nice

%O 1,4

%A _David W. Wilson_, Jan 12 2001